Question: Simplify. Rewrite the expression in the form $a^n$. $\dfrac{a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}=$
Explanation: $\dfrac{a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}= \dfrac {a^7}{a^6}$ $\begin{aligned} \dfrac{a^{7}}{a^6}&=\dfrac{\overbrace{\cancel a\cdot \cancel a\cdot \cancel a\cdot \cancel a\cdot \cancel a\cdot \cancel a\cdot a}^\text{7 times}}{\underbrace{\cancel a\cdot \cancel a\cdot \cancel a\cdot \cancel a\cdot \cancel a\cdot \cancel a}_\text{6 times}} \\\\\\ &=\underbrace{a}_\text{1 time} \\\\ \end{aligned}$ When powers have the same base $\dfrac{x^m}{x^n}=x^{m-n}$. $\begin{aligned} \dfrac{a^{7}}{a^6}&=a^{7-6} \\\\ &=a^1 \end{aligned}$ $\dfrac{a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}=a^1$